Four areas of research in theoretical population genetics are proposed. The first entails development and mathematical analysis of models for the population dynamics of short sequence repeats, microsatellites. Estimators of demographic and phylogenetic parameters will be designed that are appropriate for realistic models of the mutational processes of microsatellites. These models include bounds on the number of repeats and size-dependence in the rate and type of mutation. Statistical properties of these estimators will be studied. These estimators are often used to infer times of divergence between groups and extent of subdivision in a metapopulation. A statistical test is proposed to detect heterogeneity in mutation processes or selection among populations and microsatellite loci. A likelihood method will be used to jointly assess the growth rate of a population and the time of the most recent common ancestor from datasets of Y-chromosome microsatellite polymorphisms. The second project will develop new models for genomic imprinting. Modifiers of the extent of inactivation of target genes will be studied. The role of ploidy in the evolution of imprinting and conditions for the maintenance of partial inactivation and polymorphism for the extent of imprinting will be determined. The third area concerns mathematical models of traits that are partly genetic and partly cultural in origin. The first of these addresses the extent to which the avoidance of incest is genetically or culturally determined and uses brother-sister mating as an example. The second attempts to take account of the fact that the members of a population form part of the selective environment, rather than being passively affected by it. This new theory, called niche construction, takes the effects of one set of loci or traits as agents that influence selection on other genes. These effects may last for many generations. We plan to study the effect of culturally transmitted behaviors whose effects, current and historical, may influence the fitness of specific genotypes or one or more loci. The fourth area of study concerns the effect of the reduction in number of mitochondria during intergenerational transmission on the long-and short-term genetic integrity of mitochondria.